Prime p₀= 429565712796807857 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 52 2 16 2 178 2 28 2 58 2 (?)
a_n: 0 2 54 56 72 74 252 254 282 284 342 344
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 344
Found by: Cruncher Pete
db: batch=70, k=12, 52 16 178 28 58

SPT(14)	429565624294809451	0 40 70 78 88 100 102 106 108 120 130 138 168 208	-88501998406
SPT(14)	429565644062340757	0 30 76 90 100 102 130 156 184 186 196 210 256 286	-68734467100
SPT(14)	429565651298849629	0 28 42 78 100 124 204 208 288 312 334 370 384 412	-61497958228
TPT(12)	429565658154825779	0 2 30 32 138 140 168 170 252 254 312 314	-54641982078
SPT(14)	429565658404517797	0 16 22 30 54 82 100 126 144 172 196 204 210 226	-54392290060
SPT(14)	429565695548175419	0 2 24 38 60 72 164 168 260 272 294 308 330 332	-17248632438
TPT(12)	429565729079410751	0 2 18 20 36 38 48 50 240 242 246 248	16282602894
SPT(14)	429565756729070083	0 90 94 100 136 156 174 286 304 324 360 366 370 460	43932262226
SPT(14)	429565759073055281	0 18 32 56 66 68 96 122 150 152 162 186 200 218	46276247424
SPT(14)	429565773432962911	0 10 28 52 66 118 162 196 240 292 306 330 348 358	60636155054
SPT(14)	429565797640827011	0 36 38 66 72 80 156 182 258 266 272 300 302 338	84844019154